Ken's POTW

Peg Solitaire

The peg-solitaire game of Hi-Q (in the form of a cross) is whimsically
dissected and solved at
Cut-The-Knot's Peg Solitaire Page. That game inspired
me to dig up some others:

This game starts
with 15 pegs in the form of an equilateral triangle with a base of five pegs.
Each move consists of jumping one peg over an existing peg into
an empty position.
(Jumps are parallel to any of the three sides of the triangle.)
The jumped peg is then removed from the board.
The goal of the game is to be left with only one peg, preferably
left in the original empty hole.

What is the largest number of pegs that can be left on the board
with no moves left (no possible jumps)? You can choose the starting
position by removing any peg.

How many different starting positions exist? Try to solve the
original game for all of them.

In a 5x5 grid of squares, the center nine squares each have
one peg, numbered 1 (in the second row, second column) through
8 clockwise around the center square numbered 9.
Each number represents a piece that can jump over any other
piece, either vertically, horizontally or diagonally into an
empty square beyond.
Each piece is removed when it is jumped.

How can all the pegs be removed, except
the 9, which ends up in its original position
in the center? What is the smallest number of pegs you need to touch?

Disregarding the end position:

What is the smallest number of pegs you need to touch?

What is
the smallest number of times you need to change jumping pegs?

Can the problem be solved without diagonal jumps?
If not, what is the smallest number of diagonal
jumps needed?